{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VO7UAKEM4CDCCJLJA6ZMKUN3H5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1b2cfcc6a3b21f17010cf29a352e9186dac738e462c8a9cace3364f20e660f82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-29T15:47:25Z","title_canon_sha256":"2d62fa3a1cffd432b0ffd88ad3dbfb57e15f27b7ed74867c9b1a3cc668fd5785"},"schema_version":"1.0","source":{"id":"1111.6861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.6861","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"arxiv_version","alias_value":"1111.6861v1","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.6861","created_at":"2026-05-18T04:07:28Z"},{"alias_kind":"pith_short_12","alias_value":"VO7UAKEM4CDC","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VO7UAKEM4CDCCJLJ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VO7UAKEM","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c21391396821a4217d323ab2b870e22a0f795ddb8307999471f16ada150b59df","target":"graph","created_at":"2026-05-18T04:07:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved. In this paper, we prove that if the manifold with the critical point metric has harmonic curvature, then it is isometric to a standard sphere.","authors_text":"Gabjin Yun, Jeongwook Chang, Seungsu Hwang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-29T15:47:25Z","title":"Total Scalar Curvature and Harmonic Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6861","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4e99e92c1374d2dc04257351c60256a1a24b5ad2cc7d1f026d99c9f46cb0953c","target":"record","created_at":"2026-05-18T04:07:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1b2cfcc6a3b21f17010cf29a352e9186dac738e462c8a9cace3364f20e660f82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-11-29T15:47:25Z","title_canon_sha256":"2d62fa3a1cffd432b0ffd88ad3dbfb57e15f27b7ed74867c9b1a3cc668fd5785"},"schema_version":"1.0","source":{"id":"1111.6861","kind":"arxiv","version":1}},"canonical_sha256":"abbf40288ce08621256907b2c551bb3f68652e35a6008a2dada24fefeb2f4560","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abbf40288ce08621256907b2c551bb3f68652e35a6008a2dada24fefeb2f4560","first_computed_at":"2026-05-18T04:07:28.386520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:28.386520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iwwtbKr5wK4mfBgEQyQ8Be9dYwWE0M9VJ5qsPR5I/gC3hIUXFB30g3JiZCj+nq4LRagcAr7GquQSRiq6y0erAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:28.386954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.6861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e99e92c1374d2dc04257351c60256a1a24b5ad2cc7d1f026d99c9f46cb0953c","sha256:c21391396821a4217d323ab2b870e22a0f795ddb8307999471f16ada150b59df"],"state_sha256":"b3d754860cf0159c702610ffdd9f16695bb315856e222f4824c3dfc1df1726db"}